The usual concept of an electron worldline in Minkowski space assumes that particles have smooth time-like curves representing the movement of a centre of mass. Events are then points on the worldline and can occur with arbitrarily small inter-event spacing. Mass by itself is not a direct kinematic feature of such curves. Instead, mass and energy are input from dynamical behaviour.  An alternative model, explored in this paper is to assume that mass represents an upper bound on the frequency of special events on the worldline. This imposes a lower bound on the measure of causal regions between such events and produces two characteristic scales associated with particle mass. The scales are classical analogs of the de Broglie and Compton scales respectively. The model provides a direct basis for Feynman's original non-relativistic path-integral approach to quantum mechanics[1] as well as his relativistic chessboard model[2] and its extension to 3+1 dimensions[3].